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August 28th, 2013, 08:43 PM   #1
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How to show the standard distance in R^n is a metric space

How do I show that the standard distance in R^n is a metric space?

is a metric on ?

I know that I need to show the definition of a metric to prove this like symmetry, triangle inequality, and non-negative but I do not know how exactly to do that? It seems obvious but I don't know how to formally prove it.
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August 29th, 2013, 03:43 PM   #2
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Re: How to show the standard distance in R^n is a metric spa

Quote:
Originally Posted by jugger3
How do I show that the standard distance in R^n is a metric space?

is a metric on ?

I know that I need to show the definition of a metric to prove this like symmetry, triangle inequality, and non-negative but I do not know how exactly to do that? It seems obvious but I don't know how to formally prove it.
First what is the definition of ||x- y|| in ? As I recall it involves a square root! That pretty much takes care of "non-negative", doesn't it? And if there is such a thing as in that kind of clears "symmetric". The hard part is the "triangle inequality". But I'll bet you knew that.
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August 29th, 2013, 06:24 PM   #3
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Re: How to show the standard distance in R^n is a metric spa

Thanks HallsofIvy! I should make a better effort to always look back at the definition.
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